TABLE OF CONTENTS Linear wave theory (LWT) is the most commonly applied description for wind-generated surface gravity waves. LWT assumes that the height of the wave H is small compared to the wavelength ? (small amplitude assumption H/2 ?) and that the depth h is not small compared to the wavelength ? (finite-depth assumption h/ ?). Small amplitude LWT was originally developed by Airy (1845); and, consequently, LWT is also referred to as the Airy wave theory. In spite of the restriction of the small amplitude ratio H/2 ??1, LWT provides a reasonably good estimate of both kinematic and dynamic wave fields even when the small H/2 ? amplitude restriction is not valid! This is particularly true for estimates near the bottom of the water column where LWT satisfies exactly the kinematic bottom boundary condition (KBBC) for a horizontal, impermeable bottom boundary. In contrast, near the free surface z= ?(x, t), estimates from LWT have the largest errors. In this free surface region, more sophisticated nonlinear wave theories are required in order to obtain more accurate estimates of both kinematic and dynamic wave fields (vide., Chapter 6).
Because the LWT boundary value problem (LWT BVP) is relatively wellknown, the brief review given here in two-dimensions (x, z) is intended to introduce the notation that is applied. The LWT BVP is analyzed with real-valued elementary transcendental functions. In contrast, the wavemaker boundary value problem in Chapter 5 and...
